/* ef_rem_pio2.c -- float version of e_rem_pio2.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */

/* __rem_pio2f(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __kernel_rem_pio2_32()
 */

#include "fdlibm.h"

/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
 */
static const __int32_t two_over_pi[] = {
    0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, 0x27, 0x57, 0xD1,
    0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41,
    0xFE, 0x51, 0x63, 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
    0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, 0xD1, 0x92, 0x1C,
    0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5,
    0x2E, 0xBB, 0x44, 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
    0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, 0x84, 0x5F, 0x8B,
    0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F,
    0xEF, 0x2F, 0x11, 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
    0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, 0x5F, 0xEA, 0x2D,
    0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7,
    0x8A, 0x52, 0x92, 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
    0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, 0xCF, 0xBC, 0x20,
    0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08,
    0x65, 0x99, 0x85, 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
    0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, 0x73, 0xA8, 0xC9,
    0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
};

/* This array is like the one in e_rem_pio2.c, but the numbers are
   single precision and the last 8 bits are forced to 0.  */
static const __uint32_t npio2_hw[] = {
    0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
    0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
    0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
    0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
    0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
    0x4242c700, 0x42490f00
};

/*
 * invpio2:  24 bits of 2/pi
 * pio2_1:   first  17 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 17 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  17 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

static const float zero = 0.0000000000e+00, /* 0x00000000 */
    half = 5.0000000000e-01, /* 0x3f000000 */
    two8 = 2.5600000000e+02, /* 0x43800000 */
    invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
    pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
    pio2_1t = 1.0804334124e-05, /* 0x37354443 */
    pio2_2 = 1.0804273188e-05, /* 0x37354400 */
    pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
    pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
    pio2_3t = 6.1232342629e-17; /* 0x248d3132 */

__int32_t
__rem_pio2f(float x, float *y)
{
    float z, w, t, r, fn;
    float tx[3];
    __int32_t i, j, n, ix, hx;
    int e0, nx;

    GET_FLOAT_WORD(hx, x);
    ix = hx & 0x7fffffff;
    if (ix <= 0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
    {
        y[0] = x;
        y[1] = 0;
        return 0;
    }
    if (ix < 0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
        if (hx > 0) {
            z = x - pio2_1;
            if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
                y[0] = z - pio2_1t;
                y[1] = (z - y[0]) - pio2_1t;
            } else { /* near pi/2, use 24+24+24 bit pi */
                z -= pio2_2;
                y[0] = z - pio2_2t;
                y[1] = (z - y[0]) - pio2_2t;
            }
            return 1;
        } else { /* negative x */
            z = x + pio2_1;
            if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
                y[0] = z + pio2_1t;
                y[1] = (z - y[0]) + pio2_1t;
            } else { /* near pi/2, use 24+24+24 bit pi */
                z += pio2_2;
                y[0] = z + pio2_2t;
                y[1] = (z - y[0]) + pio2_2t;
            }
            return -1;
        }
    }
    if (ix <= 0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
        t = fabsf(x);
        n = (__int32_t)(t * invpio2 + half);
        fn = (float)n;
        r = t - fn * pio2_1;
        w = fn * pio2_1t; /* 1st round good to 40 bit */
        if (n < 32 && (ix & 0xffffff00) != npio2_hw[n - 1]) {
            y[0] = r - w; /* quick check no cancellation */
        } else {
            __uint32_t high;
            j = ix >> 23;
            y[0] = r - w;
            GET_FLOAT_WORD(high, y[0]);
            i = j - ((high >> 23) & 0xff);
            if (i > 8) { /* 2nd iteration needed, good to 57 */
                t = r;
                w = fn * pio2_2;
                r = t - w;
                w = fn * pio2_2t - ((t - r) - w);
                y[0] = r - w;
                GET_FLOAT_WORD(high, y[0]);
                i = j - ((high >> 23) & 0xff);
                if (i > 25) { /* 3rd iteration need, 74 bits acc */
                    t = r; /* will cover all possible cases */
                    w = fn * pio2_3;
                    r = t - w;
                    w = fn * pio2_3t - ((t - r) - w);
                    y[0] = r - w;
                }
            }
        }
        y[1] = (r - y[0]) - w;
        if (hx < 0) {
            y[0] = -y[0];
            y[1] = -y[1];
            return -n;
        } else
            return n;
    }
    /*
     * all other (large) arguments
     */
    if (!FLT_UWORD_IS_FINITE(ix)) {
        y[0] = y[1] = x - x;
        return 0;
    }
    /* set z = scalbn(|x|,ilogb(x)-7) */
    e0 = (int)((ix >> 23) - 134); /* e0 = ilogb(z)-7; */
    SET_FLOAT_WORD(z, ix - ((__int32_t)e0 << 23));
    for (i = 0; i < 2; i++) {
        tx[i] = (float)((__int32_t)(z));
        z = (z - tx[i]) * two8;
    }
    tx[2] = z;
    nx = 3;
    while (tx[nx - 1] == zero)
        nx--; /* skip zero term */
    n = __kernel_rem_pio2f(tx, y, e0, nx, 2, two_over_pi);
    if (hx < 0) {
        y[0] = -y[0];
        y[1] = -y[1];
        return -n;
    }
    return n;
}
